Problem: Solve for $x$ and $y$ using elimination. ${-2x+y = -12}$ ${-5x-4y = -69}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${-8x+4y = -48}$ $-5x-4y = -69$ Add the top and bottom equations together. $-13x = -117$ $\dfrac{-13x}{{-13}} = \dfrac{-117}{{-13}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-2x+y = -12}\thinspace$ to find $y$ ${-2}{(9)}{ + y = -12}$ $-18+y = -12$ $-18{+18} + y = -12{+18}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-5x-4y = -69}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ - 4y = -69}$ ${y = 6}$